Question

this graph shows a function.
mias trip to the store
which of the following stories could describe the graph? select all that apply.
mia drove 9 miles to the grocery store in 15 minutes. then, she shopped for 30 minutes. after that, she drove home in 50 minutes.
mia drove 9 miles to the grocery store in 15 minutes. then, she shopped for 15 minutes. after that, she drove home in 20 minutes.
mia drove for 9 minutes to the grocery store at a speed of 15 miles per hour. then, she shopped for 30 minutes. after that, she drove home at a speed of 20 miles per hour.
mia drove for 15 minutes to the grocery store at a speed of 36 miles per hour. then, she shopped for 15 minutes. after that, she drove home at a speed of 27 miles per hour.

Explanation:

Step1: Analyze the time - related information

The graph shows that the time taken to reach the store (the increasing part of the graph) is from \(t = 0\) to \(t=15\) minutes. The time spent shopping (the horizontal part of the graph) is from \(t = 15\) to \(t = 30\) minutes (a duration of \(30 - 15=15\) minutes). The time taken to return home (the decreasing part of the graph) is from \(t = 30\) to \(t = 50\) minutes (a duration of \(50 - 30 = 20\) minutes).

Step2: Analyze the speed - related information

We use the formula \(v=\frac{d}{t}\), where \(v\) is speed, \(d\) is distance, and \(t\) is time.

• For the trip to the store: The distance \(d = 9\) miles and \(t=15\) minutes \(=\frac{15}{60}=\frac{1}{4}\) hours. Using \(v=\frac{d}{t}\), we get \(v=\frac{9}{\frac{1}{4}}=36\) miles per hour.
• For the trip back home: The distance \(d = 9\) miles and \(t = 20\) minutes \(=\frac{20}{60}=\frac{1}{3}\) hours. Using \(v=\frac{d}{t}\), we get \(v=\frac{9}{\frac{1}{3}} = 27\) miles per hour.

Answer:

Mia drove 9 miles to the grocery store in 15 minutes. Then, she shopped for 15 minutes. After that, she drove home in 20 minutes.
Mia drove for 15 minutes to the grocery store at a speed of 36 miles per hour. Then, she shopped for 15 minutes. After that, she drove home at a speed of 27 miles per hour.